Practice question · Put in order
Order these vector spaces by how many real numbers it takes to specify one element, fewest first.
- Quadratics, written as a + bx + cx squared
- 3x2 matrices
- The plane, that is all pairs (x, y)
- 2x2 matrices
Hints
- For each space, ask how many independent choices build a general element.
- A polynomial of degree at most 2 needs one coefficient for each of 1, x and x squared.
Show the answer
- The plane, that is all pairs (x, y)
- Quadratics, written as a + bx + cx squared
- 2x2 matrices
- 3x2 matrices
Why
The counts are 2, 3, 4 and 6. Polynomials of degree at most 2 need three coefficients, so they need MORE numbers than the plane but fewer than a 2x2 matrix, the objects look nothing alike, yet this count is the only thing that distinguishes them structurally.
Practise Vector Spaces
The app has 5 more questions on this lesson, and keeps your place in the course. Mathematics I is free to start.
More questions on Vector Spaces
- Polynomials of degree at most 2, 2x3 matrices, and arrows in the plane are studied as one subject. Why is it…
- The solutions of a linear differential equation form a vector space. Why is noticing that worth anything to…
- Select every set that IS a vector space under the usual operations.
- The set of all real-valued functions f with f(2) = 0 is a vector space under pointwise addition and scaling.
- A vector space must be closed under addition and scaling and must contain a zero vector. Sort each set, taken…